%I #9 Mar 30 2012 18:58:12

%S 2,5,9,11,14,18,21,23,27,30,33,36,39,42,45,48,51,55,57,60,64,67,69,73,

%T 76,79,82,85,88,91,94,97,101,103,106,110,113,115,119,122,125,128,131,

%U 134,137,140,143,147,149,152,156,159,161,165,168,170,174,177

%N n+[nr/s]+[nt/s], where []=floor, r=3, s=sqrt(3), t=1/s.

%C The sequences A206903, A206904, A206905 partition the positive integers. To generate them, jointly rank the sets {n/3}, {n/sqrt(3)}, {n*sqrt(3)} for n>=1. The positions of n/3 in the joint ranking form A206903, and likewise for the other sequences.

%t r = 3; s = Sqrt[3]; t = 1/s;

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t];

%t Table[a[n], {n, 1, 70}] (* A206903 *)

%t Table[b[n], {n, 1, 70}] (* A206904 *)

%t Table[c[n], {n, 1, 70}] (* A206905 *)

%Y Cf. A206903, A206905.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 13 2012